The union balloted members after it received no assurances that cuts to children’s and adults’ services would not result in redundancies.

The council has already identified £10m in savings from children’s services, including £570,000 from a staffing restructure and £400,000 from freezing out-of-authority accommodation placements, but still faces a projected deficit of almost £4m.

Its health and social care department still faces a projected deficit of £0.9m, having identified cuts of £4.7m, including over £1.3m from a recruitment freeze, over £0.8m from restricting care home placements and over £0.5m from increasing eligibility thresholds for home care.

Edinburgh councillors will be asked to approve further savings at next Thursday’s meeting.

Unison branch secretary George Lee said: “You cannot make cuts of up to £16m without the threat of redundancies among the people delivering those services.”

However, council leader Jenny Dawe said: “This is very disappointing news, especially given that Unison has not chosen to discuss its concerns with us further. The council faces a serious financial situation but we are determined to take the action necessary to address the overspend.”